Do the adopted prayer times (such as the Umm Al-Qura University calendar) represent the beginning of the true dawn or the false dawn, and is it permissible to pray Fajr immediately after the Adhan, or must one wait for a period?

The fundamental principle for knowing prayer times is based on the legal signs. The time for Fajr prayer begins with the appearance of the true dawn (al-fajr al-sadiq), whose light spreads horizontally from right to left, and the prayer is valid at that point. If it is difficult to ascertain this, there is no harm in relying on approved calendars that specify the time of the true dawn in the particular country. However, one must be careful not to rely on calendars from other countries that differ from the timing of the aforementioned country.